Sentence examples for be a closed pointed from inspiring English sources

Theorem 3.2 Let K be a closed pointed convex cone in R n with int K ∗ ≠ ∅.

Let be a topological vector space and let be a closed pointed convex cone in,.

Theorem 3.1 Let K be a closed pointed convex cone in R n with K ∗ ⊆ K and int K ∗ ≠ ∅.

Definition 4.2 Let K be a closed pointed convex cone in a Hilbert space H with int K ∗ ≠ ∅.

Let be a topological semilattice or a -convex subset of a topological semilattice, let be a Hausdorff topological vector space, and let be a closed, pointed, and convex cone with.

We now introduce a new notion of -exceptional family of elements (for short, -EFE) for the pair ( f, g ) with respect to K. Definition 3.2 Let K be a closed pointed convex cone in R n with int K ∗ ≠ ∅.

Assume that,,, and such that, for any, is a closed, pointed, and convex cone in and.

Let be with nonempty -convex values, let and be mappings, and let be a mapping such that, for each, is a closed, pointed, and convex cone in with.

Let be with nonempty -convex values, and let and be mappings and be a mapping such that, for each, is a closed, pointed, and convex cone in with.

If for all, where is a closed, pointed, and convex cone in, then Corollary 3.7 coincides with Theorem of Chen and Yang [4].

It is easy to see that, if for all, where is a closed, pointed, and convex cone in, then is inclusive with respect to.